Simplify the following expression: $\sqrt{176}+\sqrt{11}-\sqrt{99}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{176}+\sqrt{11}-\sqrt{99}$ $= \sqrt{16 \cdot 11}+\sqrt{11}-\sqrt{9 \cdot 11}$ Separate the radicals and simplify. $= \sqrt{16} \cdot \sqrt{11}+\sqrt{11}-\sqrt{9} \cdot \sqrt{11}$ $= 4\sqrt{11}+\sqrt{11}-3\sqrt{11}$ Finally, simplify by combining the terms. $= ( 4 + 1 - 3 )\sqrt{11} = 2\sqrt{11}$